# Integrating Belief Domains into Probabilistic Logic Programs

arXiv: https://arxiv.org/abs/2507.17291 · HTML: https://mlsanity.com/paper/2507.17291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 30 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)
- [On the Semantics and Complexity of Probabilistic Logic Programs](https://mlsanity.com/paper/1701.09000/) (2017)
- [Efficient Inference and Learning in a Large Knowledge Base: Reasoning with Extracted Information using a Locally Groundable First-Order Probabilistic Logic](https://mlsanity.com/paper/1404.3301/) (2014)
- [LPMLN, Weak Constraints, and P-log](https://mlsanity.com/paper/2506.12784/) (2025)

## Abstract (arXiv)

Probabilistic Logic Programming (PLP) under the Distribution Semantics is a leading approach to practical reasoning under uncertainty. An advantage of the Distribution Semantics is its suitability for implementation as a Prolog or Python library, available through two well-maintained implementations, namely ProbLog and cplint/PITA. However, current formulations of the Distribution Semantics use point-probabilities, making it difficult to express epistemic uncertainty, such as arises from, for example, hierarchical classifications from computer vision models. Belief functions generalize probability measures as non-additive capacities, and address epistemic uncertainty via interval probabilities. This paper introduces interval-based Capacity Logic Programs based on an extension of the Distribution Semantics to include belief functions, and describes properties of the new framework that make it amenable to practical applications.